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1.
A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m
2/(m
1+m
2). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of . 相似文献
2.
P. G. Kazantzis 《Astrophysics and Space Science》1979,61(2):477-486
Families of three-dimensional axisymmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (v = 1,b
v = 0) of the basic plane familiesi andI. Further the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
3.
We compare families of simple periodic orbits of test particles in the Newtonian and relativistic problems of two fixed centers (black holes). The Newtonian problem is integrable, while the relativistic problem is highly non-integrable.The orbits are calculated on the meridian plane through the fixed centersM
1 (atz=+1) andM
2 (atz=–1) for energies smaller than the escape energyE=1. We use prolate spheroidal coordinates (, , =const) and also the variables =cosh and =–cos . The orbits are inside a curve of zero velocity (CZV). The Newtonian orbits are also limited by an ellipse and a hyperbola, or by two eillipses. There are 3 main types of periodic orbits (1) elliptic type (around both centers), (2) hyperbolic-type, and (3) resonant-type.The elliptic type orbits are stable in the Newtonian case and both stable and unstable in the relativistic case. From the stable orbits bifurcate double period orbits both symmetric and asymmetric with respect to thez-axis. There are also higher order bifurcations. The hyperbolic-type orbits are unstable. The Newtonian resonant orbits are defined by the ratiot
µ/t
=n/m of oscillations along and during one period, and they are all marginally unstable. The corresponding relativistic orbits are stable, or unstable. The main families are figure eight orbits aroundM
1, or aroundM
2 (3/1 orbits); gamma, or inverse gamma orbits (4/2); higher resonant families 5/1,7/1,...,8/2,12/2,...;, more complicated orbits, like 5/3, and bifurcations from the above orbits. Satellite orbits aroundM
1, orM
2, and their bifurcations (e.g. double period) exist in the relativistic case but not in the Newtonian case. The characteristics of the various families are quite different in the Newtonian and the relativistic cases. The sizes of the orbits and their stabilities are also quite different in general. In the Appendix we study the various types of straight line orbits and prove that some subcases introduced by Charlier (1902) are impossible. 相似文献
4.
E.A. Perdios 《Astrophysics and Space Science》2001,278(4):405-407
The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A1 regions for oblate larger primary, A
1 beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A
1values. 相似文献
5.
Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination. 相似文献
6.
S. T. Revankar 《Astrophysics and Space Science》1982,86(1):13-23
Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations
B
intensity of magnetic field
-
G
Grashof number
-
H
magnetic field parameter,H=(M+1/4)
1/2–1/2
-
M
magnetic field parameter
-
N
u
Nusselt number
-
P
Prandtl number of the fluid
-
r
suction parameter
-
T
temperature of the fluid
-
T
w
temperature of the plate
-
T
temperature of the fluid at infinity
-
t
time
-
t
non-dimensional time
-
u
velocity of the fluid parallel to the plate
-
u
non-dimensional velocity
-
U
velocity of the free stream
-
suction velocity
- 1
suction velocity att0
- 2
suction velocity att>0
-
x,y
coordinate axes parallel and normal to the plate, respectively
-
y
non-dimensional distance normal to the plate
-
coefficient of volume expansion
-
thermal diffusivity
-
kinematic viscosity
-
electric conductivity of the fluid
-
density of the fluid
-
non-dimensional temperature of the fluid
-
shear stress at the plate
-
non dimensional shear stress
- erf
error function
- erfc
complementary error function 相似文献
7.
Kathleen Connor Howell 《Celestial Mechanics and Dynamical Astronomy》1984,32(1):53-71
A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing . 相似文献
8.
We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E
kin/E
pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits. 相似文献
9.
We consider the bifurcation of 3D periodic orbits from the plane of motion of the primaries in the restricted three-body problem with oblateness. The simplest 3D periodic orbits branch-off at the plane periodic orbits of indifferent vertical stability. We describe briefly suitable numerical techniques and apply them to produce the first few such vertical-critical orbits of the basic families of periodic orbits of the problem, for varying mass parameter and fixed oblateness coefficent A1 = 0.005, as well as for varying A1 and fixed = 1/2. The horizontal stability of these orbits is also determined leading to predictions about the stability of the branching 3D orbits. 相似文献
10.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》1986,38(1):1-22
We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b1 and b2 as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes. 相似文献
11.
P. G. Kazantzis 《Astrophysics and Space Science》1979,65(2):493-513
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (
v
= –1,c
v
),c
v=0) of the basic plane familiesi,g
1,g
2,h,a,m andl. Further the numerical procedure employed in the determination of these families has been described and interesting results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
12.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1983,30(4):373-383
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies
j
2
(m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2–
j
2
|<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of
j
2
(m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL
3.In a similar manner, the family () can be extended to the horseshoe branch 1<2
2
2
. 相似文献
13.
An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature
c
p
specific heat at constant pressure
-
e
electrical charge
-
E
Eckert number
-
E
electrical field intensity
-
g
acceleration due to gravity
-
G
Grashof number
-
H
0
applied magnetic field
-
H
magnetic field intensity
- (j
x
, j
y
, j
z
)
components of current densityJ
-
J
current density
-
K
permeability of porous medium
-
M
magnetic parameter
-
m
Hall parameter
-
n
e
electron number density
-
P
Prandtl number
-
q
velocity vector
- (T, T
w
, T
)
temperature
-
t
time
- (u, v, w)
components of the velocity vectorq
-
U
0
uniform velocity
-
v
0
suction velocity
- (x, y, z)
Cartesian coordinates
Greek Symbols
angle
-
coefficient of volume expansion
- e
cyclotron frequency
-
frequency
-
dimensionless temperature
-
thermal conductivity
-
coefficient of viscosity
-
magnetic permeability
-
kinematic viscosity
-
mass density of fluid
- e
charge density
-
electrical conductivity
- e
electron collision time 相似文献
14.
Frank Q. Orrall 《Solar physics》1972,23(1):30-46
An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z
and if (z) and p(z) are not too rapidly varying, then
(t) m
(z
, t)+N
p(z
, t) where m
and N
depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
15.
P. G. Kazantzis 《Astrophysics and Space Science》1980,69(2):353-368
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (
v
= – 1, b
v
– 0) of the basic plane familiesi, g
1, g2, c andI. Further, the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
16.
Using the see-saw mechanism and estimation of the hypothetical mass of the electron neutrinom
e we find the hypothetical mass of muon neutrinom
µ and hypothetical mass of the tau neutrinom
. 相似文献
17.
Hong-Nan Zhou 《Astrophysics and Space Science》1988,141(2):199-206
The contact binary system CC Com (=12h09m33s.8, =+22°4339, (1950);V
max=11.31, (B-V)max=1.24) is a W UMa-type system with the shortest known period. The photometric solution of CC Com is presented using the Wilson and Devinney method. The results show that the CC Com belongs to the late-type eclipsing binary with the spectral type K5V and K6V, low temperatureT
1=4300 K,T
2=4265 K, the mass ratioq=0.5873±0.0021, and the inclinationi=87°.719±1°.44. The best regions of the gravity darkening exponents , the bolomotric albedov, and the limb-darkening coefficients are tested. It is found that 0.1250.065, 0.1v0.5, =0.5 are better regions for CC Com. The third body ofl
3 is not found to be significant. The results are combined with the spectroscopic results of Rucinski to provide an estimate of the absolute parameters. 相似文献
18.
Satoshi Hinata 《Astrophysics and Space Science》1978,55(2):427-439
We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (103109 eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f()
–5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping),
M
8×106, corresponds to the upper cut-off energy of the -ray spectrum, 109 eV. The lower limit to the momentum,
m
1.8×105, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation. 相似文献
19.
A limiting case of the problem of three bodies (m
0,m
1,m
2) is considered. The distance between the bodiesm
0 andm
1 is assumed to be much less than that between their barycenter and the bodym
2 so that one may use Hill's approximation for the potential of interaction between the bodiesm
1 andm
2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm
1 andm
2, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm
0 andm
1 takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.
m 0,m 1,m 2. , m 0 m 1. m 2, m 1 m 2 m 1 m 2 . , . . , m 0 m 1. , . .相似文献
20.
The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order 4, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = 2/2G
c
and a relativity parameter, =p
c
/
c
C
2
, wherep
c
and c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order
2. The critical rotation parameterv
c
, which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5. 相似文献